Closure statistics in interferometric data

Interferometric visibilities, reflecting the complex correlations between signals recorded at antennas in an interferometric array, carry information about the angular structure of a distant source. While unknown antenna gains in both amplitude and phase can prevent direct interpretation of these measurements, certain combinations of visibilities called closure phases and closure amplitudes are independent of antenna gains and provide a convenient set of robust observables. However, these closure quantities have subtle noise properties and are generally both linearly and statistically dependent. These complications have obstructed the proper use of closure quantities in interferometric analysis, and they have obscured the relationship between analysis with closure quantities and other analysis techniques such as self calibration. We review the statistics of closure quantities, noting common pitfalls that arise when approaching low signal-to-noise due to the nonlinear propagation of statistical errors. We then develop a strategy for isolating and fitting to the independent degrees of freedom captured by the closure quantities through explicit construction of linearly independent sets of quantities along with their noise covariance in the Gaussian limit, valid for moderate signal-to-noise, and we demonstrate that model fits have biased posteriors when this covariance is ignored. Finally, we introduce a unified procedure for fitting to both closure information and partially calibrated visibilities, and we demonstrate both analytically and numerically the direct equivalence of inference based on closure quantities to that based on self calibration of complex visibilities with unconstrained antenna gains.Comment: 31 pages, 17 figure

Bayesian Accretion Modeling: Axisymmetric Equatorial Emission in the Kerr Spacetime

The Event Horizon Telescope (EHT) has produced images of two supermassive black holes, Messier~87* (M 87*) and Sagittarius~A* (Sgr A*). The EHT collaboration used these images to indirectly constrain black hole parameters by calibrating measurements of the sky-plane emission morphology to images of general relativistic magnetohydrodynamic (GRMHD) simulations. Here, we develop a model for directly constraining the black hole mass, spin, and inclination through signatures of lensing, redshift, and frame dragging, while simultaneously marginalizing over the unknown accretion and emission properties. By assuming optically thin, axisymmetric, equatorial emission near the black hole, our model gains orders of magnitude in speed over similar approaches that require radiative transfer. Using 2017 EHT M 87* baseline coverage, we use fits of the model to itself to show that the data are insufficient to demonstrate existence of the photon ring. We then survey time-averaged GRMHD simulations fitting EHT-like data, and find that our model is best-suited to fitting magnetically arrested disks, which are the favored class of simulations for both M 87* and Sgr A*. For these simulations, the best-fit model parameters are within ${\sim}10\%$ of the true mass and within ${\sim}10^\circ$ for inclination. With 2017 EHT coverage and 1\% fractional uncertainty on amplitudes, spin is unconstrained. Accurate inference of spin axis position angle depends strongly on spin and electron temperature. Our results show the promise of directly constraining black hole spacetimes with interferometric data, but they also show that nearly identical images permit large differences in black hole properties, highlighting degeneracies between the plasma properties, spacetime, and most crucially, the unknown emission geometry when studying lensed accretion flow images at a single frequency.Comment: Accepted to ApJ, 16 pages, 10 figure

The Megamaser Cosmology Project. VII. Investigating disk physics using spectral monitoring observations

We use single-dish radio spectra of known 22 GHz H$_2$O megamasers, primarily gathered from the large dataset observed by the Megamaser Cosmology Project, to identify Keplerian accretion disks and to investigate several aspects of the disk physics. We test a mechanism for maser excitation proposed by Maoz & McKee (1998), whereby population inversion arises in gas behind spiral shocks traveling through the disk. Though the flux of redshifted features is larger on average than that of blueshifted features, in support of the model, the high-velocity features show none of the predicted systematic velocity drifts. We find rapid intra-day variability in the maser spectrum of ESO 558-G009 that is likely the result of interstellar scintillation, for which we favor a nearby ($D \approx 70$ pc) scattering screen. In a search for reverberation in six well-sampled sources, we find that any radially-propagating signal must be contributing $\lesssim$10% of the total variability. We also set limits on the magnetic field strengths in seven sources, using strong flaring events to check for the presence of Zeeman splitting. These limits are typically 200--300 mG ($1\sigma$), but our most stringent limits reach down to 73 mG for the galaxy NGC 1194.Comment: Accepted for publication in Ap

Multi-frequency Black Hole Imaging for the Next-Generation Event Horizon Telescope

The Event Horizon Telescope (EHT) has produced images of the plasma flow around the supermassive black holes in Sgr A* and M87* with a resolution comparable to the projected size of their event horizons. Observations with the next-generation Event Horizon Telescope (ngEHT) will have significantly improved Fourier plane coverage and will be conducted at multiple frequency bands (86, 230, and 345 GHz), each with a wide bandwidth. At these frequencies, both Sgr A* and M87* transition from optically thin to optically thick. Resolved spectral index maps in the near-horizon and jet-launching regions of these supermassive black hole sources can constrain properties of the emitting plasma that are degenerate in single-frequency images. In addition, combining information from data obtained at multiple frequencies is a powerful tool for interferometric image reconstruction, since gaps in spatial scales in single-frequency observations can be filled in with information from other frequencies. Here we present a new method of simultaneously reconstructing interferometric images at multiple frequencies along with their spectral index maps. The method is based on existing Regularized Maximum Likelihood (RML) methods commonly used for EHT imaging and is implemented in the eht-imaging Python software library. We show results of this method on simulated ngEHT data sets as well as on real data from the VLBA and ALMA. These examples demonstrate that simultaneous RML multi-frequency image reconstruction produces higher-quality and more scientifically useful results than is possible from combining independent image reconstructions at each frequency.Comment: 25 pages, 15 figures. Accepted to Ap